He was born at Barnstaple in August 1633, the son of another Thomas Brancker, a graduate of Exeter College, Oxford, who was in 1626 a schoolmaster near Ilchester, and about 1630 head-master of the Barnstaple High School. Young Brancker matriculated at his father"s college 8 November 1652. Proceeded Bachelor of Arts 15 June 1655, and was elected a probationer fellow of Exeter 30 June 1655, and full fellow 10 July 1656.
The family originally bore the name of Brouncker. He then retired to Cheshire, changed his views, and applied for and obtained episcopal ordination. He became a minister at Whitegate, Cheshire, but his reputation as a mathematician reached William Brereton, 3rd Baron Brereton, who gave him the rectory of Tilston, near Malpas, in 1668.
He resigned the benefice after a few months, and became head-master of the grammar school at Macclesfield, where he died in November 1676.
He was buried in Macclesfield church, and the inscription on his monument states that he was a linguist as well as a mathematician, chemist, and natural philosopher, and that he pursued studies under Robert Boyle. The youngest son, Benjamin, became a gold and silversmith in Liverpool and was the grandfather of Peter Whitfield Brancker, Mayor of Liverpool (1801).
